Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

Determination of the degradation kinetics of anthocyanins in a model juice system using isothermal and non-isothermal methods

The effect of temperature on the degradation of blackcurrant anthocyanins in a model juice system was determined over a temperature range of 4–140 °C. The thermal degradation of anthocyanins followed pseudo first-order kinetics. From 4–100 °C an isothermal method was used to determine the kinetic parameters. In order to mimic the temperature profile in retort systems, a non-isothermal method was applied to determine the kinetic parameters in the model juice over the temperature range 110–140 °C. The results from both isothermal and non-isothermal methods fit well together, indicating that the non-isothermal procedure is a reliable mathematical method to determine the kinetics of anthocyanin degradation. The reaction rate constant (k) increased from 0.16 (±0.01) × 10−3 to 9.954 (±0.004) h−1 at 4 and 140 °C, respectively. The temperature dependence of the rate of anthocyanin degradation was modelled by an extension of the Arrhenius equation, which showed a linear increase in the activation energy with temperature.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

A METHOD FOR THE STUDY OF ACCRETION DISK EMISSION IN CATACLYSMIC VARIABLES. I. THE MODEL

We have developed a spectrum synthesis method for modeling the ultraviolet (UV) emission from the accretion disk from cataclysmic variables (CVs). The disk is separated into concentric rings, with an internal structure from the Wade & Hubeny disk-atmosphere models. For each ring, a wind atmosphere is calculated in the comoving frame with a vertical velocity structure obtained from a solution of the Euler equation. Using simple assumptions, regarding rotation and the wind streamlines, these one-dimensional models are combined into a single 2.5-dimensional model for which we compute synthetic spectra. We find that the resulting line and continuum behavior as a function of the orbital inclination is consistent with the observations, and verify that the accretion rate affects the wind temperature, leading to corresponding trends in the intensity of UV lines. In general, we also find that the primary mass has a strong effect on the P Cygni absorption profiles, the synthetic emission line profiles are strongly sensitive to the wind temperature structure, and an increase in the mass-loss rate enhances the resonance line intensities. Synthetic spectra were compared with UV data for two high orbital inclination nova-like CVs-RW Tri and V347 Pup. We needed to include disk regions with arbitrary enhanced mass loss to reproduce reasonably well widths and line profiles. This fact and a lack of flux in some high ionization lines may be the signature of the presence of density-enhanced regions in the wind, or alternatively, may result from inadequacies in some of our simplifying assumptions.

CDM accelerating cosmology as an alternative to Lambda CDM model

A new accelerating cosmology driven only by baryons plus cold dark matter (CDM) is proposed in the framework of general relativity. In this scenario the present accelerating stage of the Universe is powered by the negative pressure describing the gravitationally-induced particle production of cold dark matter particles. This kind of scenario has only one free parameter and the differential equation governing the evolution of the scale factor is exactly the same of the Lambda CDM model. For a spatially flat Universe, as predicted by inflation (Omega(dm) + Omega(baryon) = 1), it is found that the effectively observed matter density parameter is Omega(meff) = 1 - alpha, where alpha is the constant parameter specifying the CDM particle creation rate. The supernovae test based on the Union data (2008) requires alpha similar to 0.71 so that Omega(meff) similar to 0.29 as independently derived from weak gravitational lensing, the large scale structure and other complementary observations.

A flexible model for survival data with a cure rate: a Bayesian approach

In this paper we deal with a Bayesian analysis for right-censored survival data suitable for populations with a cure rate. We consider a cure rate model based on the negative binomial distribution, encompassing as a special case the promotion time cure model. Bayesian analysis is based on Markov chain Monte Carlo (MCMC) methods. We also present some discussion on model selection and an illustration with a real dataset.

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors Sufficient conditions for attaining consistent estimators for model parameters are presented Asymptotic distributions for the line regression estimators are derived Applications to the elliptical class of distributions with two error assumptions are presented The model generalizes previous results aimed at univariate scenarios (C) 2010 Elsevier Inc All rights reserved

Chinese Basic Pension Substitution Rate: A Monte Carlo Demonstration of the Individual Account Model

At the end of 2005, the State Council of China passed ”The Decision on adjusting the Individual Account of Basic Pension System”, which adjusted the individual account in the 1997 basic pension system. In this essay, we will analyze the adjustment above, and use Life Annuity Actuarial Theory to establish the basic pension substitution rate model. Monte Carlo simulation is also used to prove the rationality of the model. Some suggestions are put forward associated with the substitution rate according to the current policy.

In search of exchange rate predictability : a study about accuracy, consistency, and granger causality of forecasts generated by a Taylor Rule Model

Este estudo investiga o poder preditivo fora da amostra, um mês à frente, de um modelo baseado na regra de Taylor para previsão de taxas de câmbio. Revisamos trabalhos relevantes que concluem que modelos macroeconômicos podem explicar a taxa de câmbio de curto prazo. Também apresentamos estudos que são céticos em relação à capacidade de variáveis macroeconômicas preverem as variações cambiais. Para contribuir com o tema, este trabalho apresenta sua própria evidência através da implementação do modelo que demonstrou o melhor resultado preditivo descrito por Molodtsova e Papell (2009), o “symmetric Taylor rule model with heterogeneous coefficients, smoothing, and a constant”. Para isso, utilizamos uma amostra de 14 moedas em relação ao dólar norte-americano que permitiu a geração de previsões mensais fora da amostra de janeiro de 2000 até março de 2014. Assim como o critério adotado por Galimberti e Moura (2012), focamos em países que adotaram o regime de câmbio flutuante e metas de inflação, porém escolhemos moedas de países desenvolvidos e em desenvolvimento. Os resultados da nossa pesquisa corroboram o estudo de Rogoff e Stavrakeva (2008), ao constatar que a conclusão da previsibilidade da taxa de câmbio depende do teste estatístico adotado, sendo necessária a adoção de testes robustos e rigorosos para adequada avaliação do modelo. Após constatar não ser possível afirmar que o modelo implementado provém previsões mais precisas do que as de um passeio aleatório, avaliamos se, pelo menos, o modelo é capaz de gerar previsões “racionais”, ou “consistentes”. Para isso, usamos o arcabouço teórico e instrumental definido e implementado por Cheung e Chinn (1998) e concluímos que as previsões oriundas do modelo de regra de Taylor são “inconsistentes”. Finalmente, realizamos testes de causalidade de Granger com o intuito de verificar se os valores defasados dos retornos previstos pelo modelo estrutural explicam os valores contemporâneos observados. Apuramos que o modelo fundamental é incapaz de antecipar os retornos realizados.

Short-term temporal changes of soil carbon losses after tillage described by a first-order decay model

Tillage stimulates soil carbon (C) losses by increasing aeration, changing temperature and moisture conditions, and thus favoring microbial decomposition. In addition, soil aggregate disruption by tillage exposes once protected organic matter to decomposition. We propose a model to explain carbon dioxide (CO2) emission after tillage as a function of the no-till emission plus a correction due to the tillage disturbance. The model assumes that C in the readily decomposable organic matter follows a first-order reaction kinetics equation as: dC(sail)(t)/dt = -kC(soil)(t) and that soil C-CO2 emission is proportional to the C decay rate in soil, where C-soil(t) is the available labile soil C (g m(-2)) at any time (t). Emissions are modeled in terms soil C available to decomposition in the tilled and non-tilled plots, and a relationship is derived between no-till (F-NT) and tilled (F-Gamma) fluxes, which is: F-T = a1F(NT)e(-a2t), where t is time after tillage. Predicted and observed fluxes showed good agreement based on determination coefficient (R-2), index of agreement and model efficiency, with R-2 as high as 0.97. The two parameters included in the model are related to the difference between the decay constant (k factor) of tilled and no-till plots (a(2)) and also to the amount of labile carbon added to the readily decomposable soil organic matter due to tillage (a,). These two parameters were estimated in the model ranging from 1.27 and 2.60 (a(1)) and - 1.52 x 10(-2) and 2.2 x 10(-2) day(-1) (a(2)). The advantage is that temporal variability of tillage-induced emissions can be described by only one analytical function that includes the no-till emission plus an exponential term modulated by tillage and environmentally dependent parameters. (C) 2008 Elsevier B.V. All rights reserved.

Estimation of Maximal Work Rate Based on the 6-Minute Walk Test and Fat-Free Mass in Chronic Obstructive Pulmonary Disease

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

A model to predict R134a refrigerant leakage through the radial clearance of rolling piston compressors

In this paper a non-isothermal two-phase model for oil-R134a refrigerant mixture flow is presented to predict the R134a leakage through the radial clearance of rolling piston compressors. The flow is divided in a liquid single-phase region and in a two-phase region, in which the homogeneous model is used to simulate the flow. The refrigerant leakage is determined using the mixture mass flow rate and the refrigerant mass fraction variation along the flow. The results are obtained for inlet pressures varying from 200 to 700 kPa, inlet temperatures ranging from 40 to 60 degrees C, and minimal clearances between 10 and 60 mu m. The results are firstly compared to existing isothermal model data, showing that there is a significant difference between the leakage flow rates predicted by isothermal and non-isothermal models. Finally, a useful general equation for compressor designers is proposed to calculate the refrigerant leakage for a large range of operation conditions. (C) 2012 Elsevier Ltd and IIR. All rights reserved.

Studies on the adsorption and kinetics of photodegradation of a model compound for heterogeneous photocatalysis onto TiO2

An investigation was made on the adsorption and kinetics of photodegradation of potassium hydrogenphthalate in an aqueous suspension of TiO2. Two models, Langmuir and Freundlich, were used to describe the adsorption process and the model proposed by Langmuir-Hinshelwood (L-H) was employed to describe the kinetics of the photodecomposition reactions of hydrogenphthalate. The results of the adsorptions were fitted to the models proposed by Langmuir and Freundlich. Adsorption was found to be a function of the temperature, with adsorption capacity increasing from 2.4 to 4.5 mg/g when the temperature rose from 20 to 30 degrees C. The kinetic model indicates that the rate constant, k, of the first order reaction, is high in the 10.0 to 100 mg/l interval, which is coherent with the low value of the adsorption constant, K. The results fitted to the L-H model led to an equation that, within the range of concentrations studied here, theoretically allows one to evaluate the photodegradation rate. (c) 2005 Elsevier Ltd. All rights reserved.